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Maximize Z = 20x1 + 10x2 Subject to x1 + 2x2 ≤ 40 3x1+ x2 = 30 4x1 + 3x2 ≥ 60 and x1,x2 ≥ 0
A firm manufactures two product A & B on which the profit earned per unit are Rs. 3 and Rs. 4, respectively. Each product is processed on two machines M1 and M2. Product A requires one minute of processing time on M1and two minutes on M2, while product B requires one minute of processing time on M1 and one minute on M2. Machine M1 is available for not more than 7 hours and 30 minutes while machine M2 is available for 10 hours during any working day. Formulate the problem as LPP.
Minimize Z = -3x1 + x2 – 2x3 Subject to x1 + 3x2 +x3 ≤ 5 2x1 – x2 + x3 ≥ 2 4x1 + 3x2 -2x3 = 5 And x1,x2,x3 ≥ 0
Maximize Z = 10x1 + 15x2 Subject to 2x1 + x2 ≤ 26 2x1 + 4x2 ≤ 56 X1 – x2 ≥ -5 And x1, x2 ≥ 0
Consider the transportation problem shown in table below. Find the initial basic feasible solution using Northwest corner method.
A chemical company distributes its products by trucks loaded at its only loading station and loading station is working 24 hours, continuously. Both company’s trucks and contractor’s trucks are used for this purpose. It was find out that on an average 10 minutes one truck arrived and average loading time is 6 minutes. If 50% trucks are contractor’s trucks find:
A transportation company has 5, 10, 7 and 3 trucks available at four different sites A, B, C and D. Its customers have requirement of 5, 8 and 10 trucks at the three different destinations X, Y and Z respectively. The distance (in kms.) from an origin to destination is summarized in the following table. Formulate above problem as transportation problem and determine strategy for a company using VAM. Test the optimality of VAM solution and determine optimum strategy for the transport company. X Y Z A 70 30 60 B 40 60 80 C 50 80 40 D 80 40 30
What do you understand by zero sum with reference to game theory? Explain saddle point in brief.
A copy maker has one copy making machine and he operates as the order comes. The order arrival is poison distribution having interval time of 0.5 min. The average time to serve a copy is distributed with mean of 0.3 min. Determine the following:
Company has purchased machine A costing Rs. 4500 and it has estimated operating cost of Rs. 100 for the first year increasing by Rs. 1000 per year in the second and subsequent years. Now, after six months due to technological advancement machine B was introduced costing Rs. 5000. Its operating cost is Rs. 200 for the first year, increasing by Rs. 400 in second year and subsequent years. Now, company is thinking to buy the machine B. Suggest him optimal time. Consider resale value as zero for both machines.
Explain briefly the difference in replacement of items which deteriorates gradually and items which fails completely that too suddenly.
What is EMV? How is it computed to be used a criterion of decision making and when?
The following table give the duration in days and the predecessor for the various tasks. Draw the network diagram and find the minimum time for completion of the project.
| Task | Time (days) | Predecessor |
|---|---|---|
| A | 8 | - |
| B | 10 | - |
| C | 8 | - |
| D | 10 | A |
| E | 16 | A |
| F | 17 | B, D |
| G | 18 | C |
| H | 14 | C |
| I | 9 | F, G |
A small project is composed of 7 activities whose time estimates are listed in the table below. Activities are identified by their beginning and ending node numbers:
| Activity | |||
|---|---|---|---|
| 1-2 | 1 | 1 | 7 |
| 1-3 | 1 | 4 | 7 |
| 1-4 | 2 | 2 | 8 |
| 2-5 | 1 | 1 | 1 |
| 3-5 | 2 | 5 | 14 |
| 4-6 | 2 | 5 | 8 |
| 5-6 | 3 | 6 | 15 |
Questions repeat across sessions. Working through two or three papers shows you which topics GTU asks most.
BE Mechanical
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Official Gujarat Technological University (GTU) examination paper for Operation Research (Winter 2025, B.E. · Mechanical Engineering, Sem 5). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.
Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.
3151910 Operation Research
Official GTU PDF · Winter 2025
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